John Maynard Smith, who has died aged 84, was emeritus professor of biology at the University of Sussex and one of the world's greatest evolutionary biologists.

JMS - as he was nearly always known - was born in London, but, following the death of his surgeon father, spent most of his youth with his mother's family on and around Exmoor. His Aunt Mary gave him a copy of Edmund Sanders's A Bird Book For The Pocket, which enabled him to put a name to the birds he saw, and helped develop his passion for natural history.

JMS was rather unhappy at Eton College, but that was where he developed his other two abiding passions: mathematics and Darwinism. He then read engineering at Trinity College, Cambridge, and joined the Communist party. But when the second world war broke out in 1939, JMS ignored the party line - which, following the Hitler-Stalin pact, was that the conflict was merely an imperialist struggle - by attempting to join the army. He was rejected, later arguing that "under the circumstances, my poor eyesight was a selective advantage - it stopped me getting shot".

His contribution to the war effort, therefore, involved finishing his degree in 1941, and then applying it, from 1942 to 1947, to military aircraft design. He decided after the war, he recalled, "that aeroplanes were noisy and old-fashioned".

Thus, JMS changed direction and entered University College London to study zoology. There he studied fruit fly genetics under the great JBS Haldane, another apostate Etonian, Marxist and member of the Communist party. JMS graduated in 1951, and from 1952 to 1965 was a lecturer in zoology at UCL.

In 1956, JMS watched images of the scenes on the streets in Budapest, during the brutal suppression by the Soviet army of the Hungarian revolution. It was that which finally led him, along with many other intellectuals, out of the Communist party.

In 1962, Sussex University was established, and three years later JMS became the founding dean of its School of Biological Sciences. He held the post for an amazing seven years, until 1972, only to be re-elected in the early 1980s.

JMS helped to illuminate so many areas in biology that it is hard to know where to begin. By introducing mathematical models from game theory into the study of behaviour, he showed that the success of an individual's behaviour often depends on what other individuals do. He introduced the idea of an "evolutionarily stable strategy": a strategy that, once common, cannot be bettered by alternatives. This work has completely revolutionised the way biologists think about behavioural evolution, and game theory is now one of the most commonly used tools in evolutionary thinking.

JMS also tackled one of the most vexed - but superficially least obvious - conundrums of evolutionary biology: why has sex evolved? His book The Evolution Of Sex (1978) pointed out "the twofold cost of sex". One way to understand this cost is to notice that sexually reproducing organisms must produce both female and male offspring, whereas asexual, or clonal, organisms need only produce females. Since in most sexual populations around half the offspring produced are male, an asexual population with the same fecundity will produce twice as many daughters. This advantage applies generation after generation, seemingly providing a huge evolutionary advantage to clonal reproduction. Thus the problem is: why do we see so much sex in the world?

Like his mentor, Haldane, JMS was deeply committed to making evolutionary ideas accessible to a wide audience. His "little Penguin", The Theory Of Evolution (1958, 1966, 1975, 1993), inspired many leading researchers to become biologists.

Despite his fame, he would nevertheless take time to discuss ideas with undergraduate students and eminent professors alike. He displayed almost limitless intellectual energy, even in his 80s. On one recent occasion, a junior researcher from another university sent him a paper and included a question with it. Within a day, JMS had written three pages of detailed notes and calculations, to the questioner's surprise and appreciation.

In 1985, JMS retired from teaching and administration, but certainly not from research. He wrote the influential book The Major Transitions In Evolution (1995) with E Szathmary, and then what he called "the birdwatchers' version", aimed at a wider public, The Origins Of Life (1999). Another major focus for the final decades of his life was on the population structure and evolution of disease-causing bacteria. He revolutionised the field with an early publication, How Clonal Are Bacteria? (1993), going on to contribute to our understanding of a number of pathogens, including the bacterium causing tuberculosis in cattle and badgers.

His final book, Animal Signals, was published last year. In it, JMS strove to disentangle the complex and often confusing terminology that had characterised the subject, and then challenged the widely held assumption that there is only one correct explanation for why signallers do not "cheat". For example, if a male nightingale's beautiful song signals his quality - genetic or otherwise - to prospecting females, why do not poor quality male nightingales pretend to be better than they are?

Unsurprisingly, JMS was showered with honours. These included the 1999 Crafoord Prize (awarded by the Swedish Academy of Sciences to scientists in fields not eligible for Nobel prizes) and the 2001 Kyoto Prize, Japan's highest private award for lifetime achievement.

The University of Sussex also acknowledged his achievements, for example by renaming its biological sciences building, and the canteen within it, after him in 2003. As JMS said, it became "probably the only biology department named after its caff".

I suspect that a far greater reward was the genuine affection he inspired. As an undergraduate said to me yesterday, and talking about someone who had "retired" two decades ago: "he was such a lovely man".

JMS was famous not only for the quality of the science he produced, but also for the way in which he produced it. He had absolutely no time for academic pretensions, and had a well-honed ability to cut to the heart of debate. For JMS, the only important measure of an idea's worth was: is it true, and more importantly, is it interesting?

For most of JMS's time at Sussex, he lived at the White House on Kingston Ridge. He was an avid gardener, regularly opening his beautiful garden to the public, and making highly quaffable wine from the grapes that he grew there. Whether these alcoholic beverages were an influence on his frequently scurrilous - but always witty - limericks, I cannot tell.

My colleagues and I are feeling keenly the loss of a dear friend, whose knowledge, enthusiasm and curiosity enlivened discussions, whether in the office, in the field, or in the pub. To our despair, we can no longer directly seek his clear and patient advice. But our memories - and JMS's prodigious output of publications - will continue to inspire us, and many biologists around the world.

He is survived by his wife Sheila, their two sons and their daughter.

· John Maynard Smith, biologist, born January 6 1920; died April 19 2004